华东师范大学学报（自然科学版） >

2021 , Vol. 2021 >Issue 1: 144 - 151

DOI: https://doi.org/10.3969/j.issn.1000-5641.20202s2001

物理学与电子学

复杂网络上非马尔科夫易感-感染模型的二阶平均场求解

  • 祁婷 ,
  • 林诏华 ,
  • 冯秘 ,
  • 唐明
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  • 1. 华东师范大学 通信与电子工程学院, 上海　200241
    2. 华东师范大学 物理与电子科学学院,上海　200241
    3. 香港浸会大学 物理系, 香港　999077

收稿日期: 2020-03-03

  网络出版日期: 2021-01-28

基金资助

国家自然科学基金(11975099, 11575041)

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Second order mean field approach of non-Markovian susceptible-infected model for complex networks

  • Ting QI ,
  • Zhaohua LIN ,
  • Mi FENG ,
  • Ming TANG
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  • 1. School of Communication and Electronic Engineering, East China Normal University, Shanghai　200241, China
    2. School of Physics and Electronic Science, East China Normal University, Shanghai　200241, China
    3. Department of Physics, Hong Kong Baptist University, Hong Kong　999077, China

Received date: 2020-03-03

  Online published: 2021-01-28

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摘要

提出了一种能够描述网络传播过程的非马尔科夫特征的数学理论, 从而为控制真实世界中疾病或谣言的扩散提供理论支撑. 根据二阶平均场近似的方法, 以及通过引入闲置边的概念, 给出了能够在复杂网络上求解易感-感染(Susceptible-Infected, SI)非马尔科夫传播动力学的一系列偏微分方程组. 比较了实验模拟结果与理论计算结果, 该数学方法能够精准预测复杂网络上 SI 模型的爆发时间演化过程. 另外, 该理论还可以用来预测单个节点被感染的平均时刻, 且通过实验模拟结果证实了其正确性和准确性.

关键词： 复杂网络; 传播动力学; 非马尔科夫; 二阶平均场理论

本文引用格式

祁婷 , 林诏华 , 冯秘 , 唐明 . 复杂网络上非马尔科夫易感-感染模型的二阶平均场求解[J]. 华东师范大学学报（自然科学版）, 2021 , 2021(1) : 144 -151 . DOI: 10.3969/j.issn.1000-5641.20202s2001

Abstract

The objective of this paper is to propose a mathematical theory that can describe the non-Markovian characteristics of the network spreading process, thereby establishing theoretical support for controlling the propagation of diseases or rumors in the real world. According to the second-order mean-field approximation method and the concept of idle edges, a series of partial differential equations are presented that can be used to solve the non-Markovian spreading dynamics of a susceptible-infected (SI) model in complex networks. By comparing the simulation outputs with the theoretical results, this mathematical method can accurately predict the spreading process of the SI model on complex networks. The theory, moreover, can be used to predict the average time for a single node to be infected. The correctness and accuracy of the theory is verified by experimental simulation results.

Key words： complex network; spreading dynamics; non-Markovian; second order mean field theory

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